The long-term objectives of this proposal are to develop statistical models and methods to analyze various types of AIDS data and better understand the natural history and future spread of the epidemic. The specific aims fall into four categories: (1) to develop statistical methods for estimating the distribution of the latency period between infection by the AIDS virus and the onset of AIDS, for assessing the effects of covariates (cofactors) on this distribution, and for estimating the infection rates over time, based on data from transfusion and pediatric AIDS cases; (2) to develop statistical methods for estimating the AIDS latency distribution, for assessing the role of covariates on this distribution, and for assessing the dependence between the latencies of infected persons and of those who infected them, based on certain types of 'screening' data; (3) to develop statistical models and methods for studying, in infected persons, the deterioration in immune system over time, and the role of cofactors on this deterioration, based on repeated serologic measures of immune function; and (4) to develop statistical models for the development and spread of infection with the AIDS virus in a heterogeneous population, and to implement these models in a computer program. Techniques of survival analysis and of more general stochastic processes will play a key role in the development of these methods.